Encryption/decryption systems generally rely upon one or more cryptographic keys. In a symmetric encryption system, for example the DES (Data Encryption Standard) system, the same cryptographic key is used to encrypt and decrypt data, while in an asymmetric encryption system, for example the RSA (Rivest-Shamir-Adelman) system, different cryptographic keys are used for encryption and decryption. In an asymmetric encryption system, typically a pair of cryptographic keys are generated of which one, known as the private key, is kept secret while the other, known as the public key, is publicly available.
It is important that the cryptographic key used in a symmetric encryption system or the private key used in an asymmetric encryption system is known only by authorised personnel or devices. However, the cryptographic keys employed are typically large numbers which are difficult for a person to memorise and therefore a permanent record of the cryptographic key is generally made. This raises the problem of security of the permanent record.
The RSA algorithm generates the public and private key using a random seed number. German patent application DE 4243908A1 describes using a biometric value calculated from a biometric attribute of a person, for example a fingerprint, as the random seed number. In this way, there is no requirement to maintain a permanent record of the private key because it can be generated whenever needed by scanning the fingerprint of the person. DE 4243908A1 does not, however, describe how to generate a repeatable biometric value from an analogue data source such as a fingerprint.
A problem with the encryption system described in DE 4243908A1 is that the biometric value is uniquely associated with a private key and therefore if the private key is discovered, then the security of the encryption system is irrevocably lost. International patent publication WO 98/48538 addresses this problem and describes an encryption system in which biometric data is processed by a filter to generate directly a private key for the RSA algorithm, enabling the generated private key to be changed by using a different filter. In order to be able to generate a repeatable private key from the biometric data, for each bit of the private key the filter compares a number of binary digits, generated from the biometric data, which should be identical, and selects the binary digit which appears most often.
The present inventors have recognised that a problem with the system described in WO 98/48538 is that by constraining the repeatable number generated from the biometric data to be equal to a private key, part of the inherent randomness (sometimes called entropy) of the biometric data is sacrificed. This results in a reduction in the entropy of the generated private key.
Those skilled in the art will appreciate that it is desirable for the private key to have as much entropy as possible because this increases the difficulty of cryptoanalysing an encrypted message by trying all possible private keys.